extract the square root of 18a + 3a² = 45
Answers
Step-1 : Multiply the coefficient of the first term by the constant 1 • 45 = 45
Step-2 : Find two factors of 45 whose sum equals the coefficient of the middle term, which is -18 .
-45 + -1 = -46 -15 + -3 = -18 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -3
a2 - 15a - 3a - 45
Step-4 : Add up the first 2 terms, pulling out like factors :
a • (a-15)
Add up the last 2 terms, pulling out common factors :
3 • (a-15)
Step-5 : Add up the four terms of step 4 :
(a-3) • (a-15)
Which is the desired factorization
Equation at the end of step2:
(3 - a) • (a - 15) = 0
STEP3:Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : -a+3 = 0
Subtract 3 from both sides of the equation :
-a = -3
Multiply both sides of the equation by (-1) : a = 3
Solving a Single Variable Equation:
3.3 Solve : a-15 = 0
Add 15 to both sides of the equation :
a = 15
Supplement : Solving Quadratic Equation Directly
Solving a2-18a+45 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Answer:
45 is the ans
hope it helps u
Step-by-step explanation: